Problem $1(10$ points$)$ A fluid flows upward in an inclined circular pipe of diameter $0\mathrm{.}2$ m $,$ which has a mean roughness of $0\mathrm{.}2$ mm $.$ The flow is steady and fully developed. The volumetric flow rate is $Q=0\mathrm{.}0475\frac{m^3}{s}.$ A section of the pipe has a length of $2$ m with an elevation rise of $1$ m $.$

$($a$)$ If the fluid is SAE$50$W oil $(=902k\frac{g}{m^3},=0\mathrm{.}86k\frac{g}{m*s}),$ is this flow laminar or turbulent? If the flow is laminar, find the maximum speed. Also compute the pressure drop over this section of the pipe $(5$ points$).$

$($b$)$ If the fluid is water $(=1000k\frac{g}{m^3},=0\mathrm{.}001k\frac{g}{m*s}),$ is the flow laminar or turbulent? If the flow is laminar, find the maximum speed. Also Compute the pressure drop over this section of the pipe $(5$ points$).$